Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

This article draws from Hiroko Kawaguchi Warshauer's conceptualisation of productive struggle, which capitalises on experiences that elicit struggle, that is, those that require students to 'expend intellectual effort' and that are productive, in the sense that they seek to 'advance thinking and deepen' understanding of mathematical concepts and…

Existing literature reviews of calculus learning made an important contribution to our understanding of the development of mathematics education research in this area, particularly their documentation of how research transitioned from studying students' misconceptions to investigating students' understanding and ways of thinking per se. This paper…

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

This study consists of a categorisation of the vocabulary of chemistry, focusing on the terminological difficulties students face when learning this subject. Therefore, this classification intends to provide chemistry teachers an awareness of the language barriers students must overcome in their understanding of this scientific discipline. Two…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

This study compared sections of functions and linear functions from four Korean textbooks and Core Plus Mathematics Project (CPMP). To understand differences and similarities among these textbooks, both horizontal and vertical analyses were conducted. The horizontal analysis results revealed that topics related to functions and linear functions…

Mathematics is central in school curricula around the world, yet outcomes are mixed at best. This is true both in relation to attitudes expressed towards mathematics, and in relation to observed assessment outcomes, showing how poorly individuals are prepared to use mathematics in a world in which the ability to do so is of increasing importance.…

In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and…

Cognitively demanding tasks are at the heart of the implementation of the Common Core State Standards in Mathematics (CCSSI 2010). As with all the grades, teachers of grades 5 and 6 are challenged to use tasks that simultaneously address the grade-level Standards as well as the Standards for Mathematical Practice (SMP). Cognitively demanding tasks…

The present paper examines the difficulties Greek senior high school students identify in learning Statistics and how these difficulties are related to the course's level of difficulty. Also it examines the difficulties students identify that teachers face while teaching Statistics, their suggestions for changes and how these difficulties and…